# Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computing

arXiv: https://arxiv.org/abs/2506.05292 · HTML: https://mlsanity.com/paper/2506.05292/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 66 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Builds on (most cited first, 22 of 22)

- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [On the Implicit Bias in Deep-Learning Algorithms](https://mlsanity.com/paper/2208.12591/) (2022)
- [Generalized Teacher Forcing for Learning Chaotic Dynamics](https://mlsanity.com/paper/2306.04406/) (2023)
- [Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model](https://mlsanity.com/paper/1803.04779/) (2018)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/2201.08910/) (2022)
- [Zero-shot forecasting of chaotic systems](https://mlsanity.com/paper/2409.15771/) (2024)
- [Model scale versus domain knowledge in statistical forecasting of chaotic systems](https://mlsanity.com/paper/2303.08011/) (2023)
- [Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing](https://mlsanity.com/paper/2108.04074/) (2021)
- [Parallel Machine Learning for Forecasting the Dynamics of Complex Networks](https://mlsanity.com/paper/2108.12129/) (2021)
- [Separation of Chaotic Signals by Reservoir Computing](https://mlsanity.com/paper/1910.10080/) (2019)
- [Learning unseen coexisting attractors](https://mlsanity.com/paper/2207.14133/) (2022)
- [Catch-22s of reservoir computing](https://mlsanity.com/paper/2210.10211/) (2022)
- [Machine Learning Link Inference of Noisy Delay-coupled Networks with Opto-Electronic Experimental Tests](https://mlsanity.com/paper/2010.15289/) (2020)
- [Hybridizing Traditional and Next-Generation Reservoir Computing to Accurately and Efficiently Forecast Dynamical Systems](https://mlsanity.com/paper/2403.18953/) (2024)
- [Beyond Occam's Razor in System Identification: Double-Descent when Modeling Dynamics](https://mlsanity.com/paper/2012.06341/) (2020)
- [Inferring Attracting Basins of Power System with Machine Learning](https://mlsanity.com/paper/2305.14374/) (2023)
- [Unsupervised learning for anticipating critical transitions](https://mlsanity.com/paper/2501.01579/) (2025)
- [Teaching Recurrent Neural Networks to Modify Chaotic Memories by Example](https://mlsanity.com/paper/2005.01186/) (2020)

## Built on by (most cited first, 2 of 2)

- [ChaosNexus: A Foundation Model for ODE-based Chaotic System Forecasting with Hierarchical Multi-scale Awareness](https://mlsanity.com/paper/2509.21802/) (2025)
- [Storage and selection of multiple chaotic attractors in minimal reservoir computers](https://mlsanity.com/paper/2603.15155/) (2026)

## Abstract (arXiv)

Machine learning techniques offer an effective approach to modeling dynamical systems solely from observed data. However, without explicit structural priors -- built-in assumptions about the underlying dynamics -- these techniques typically struggle to generalize to aspects of the dynamics that are poorly represented in the training data. Here, we demonstrate that reservoir computing -- a simple, efficient, and versatile machine learning framework often used for data-driven modeling of dynamical systems -- can generalize to unexplored regions of state space without explicit structural priors. First, we describe a multiple-trajectory training scheme for reservoir computers that supports training across a collection of disjoint time series, enabling effective use of available training data. Then, applying this training scheme to multistable dynamical systems, we show that RCs trained on trajectories from a single basin of attraction can achieve out-of-domain generalization by capturing system behavior in entirely unobserved basins.